Subgroups — #62955

Order 256.

3655 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	4	yes	maximal, complemented
2	#3554	C₂	1	2	yes	maximal, complemented
3	#3548	C₂	1	2	yes	maximal, complemented
4	#3546	C₂	1	2	yes	maximal, complemented
5	#3546	C₂	1	4	yes	maximal, complemented
6	#3543	C₂	1	4	yes	maximal, complemented
7	#3543	C₂	1	2	yes	maximal, complemented
8	#3542	C₂	1	4	yes	maximal, complemented
9	#3539	C₂	1	4	yes	maximal, complemented
10	#3534	C₂	1	8	yes	maximal, complemented
11	#3519	C₂	1	2	yes	maximal, complemented
12	#3517	C₂	1	2	yes	maximal, complemented
13	#3513	C₂	1	4	yes	maximal, complemented
14	#3508	C₂	1	1	yes	maximal, characteristic, complemented
15	#3508	C₂	1	2	yes	maximal, complemented
16	#3507	C₂	1	1	yes	maximal, characteristic, complemented
17	#3506	C₂	1	2	yes	maximal, complemented
18	#3498	C₂	1	1	yes	maximal, characteristic, complemented
19	#3494	C₂	1	2	yes	maximal, complemented
20	#3488	C₂	1	2	yes	maximal, complemented
21	#3485	C₂	1	2	yes	maximal, complemented
22	#3475	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#550	C₂	1	1	yes	maximal, characteristic, complemented
25	#3461	C₂	1	1	yes	maximal, characteristic, complemented
26	#3449	C₂	1	2	yes	maximal, complemented
27	C₂×H(5,𝔽₂)	C₂²	1	2	yes	complemented
28	C₂²×#41	C₂²	1	2	yes	complemented
29	C₂²×#41	C₂²	1	2	yes	complemented
30	#562	C₂²	1	8	yes	complemented
31	#562	C₂²	1	8	yes	complemented
32	#560	C₂²	1	8	yes	complemented
33	#560	C₂²	1	8	yes	complemented
34	#560	C₂²	1	8	yes	complemented
35	#560	C₂²	1	8	yes	complemented
36	#559	C₂²	1	4	yes	complemented
37	#559	C₂²	1	4	yes	complemented
38	#559	C₂²	1	2	yes	complemented
39	#559	C₂²	1	2	yes	complemented
40	#559	C₂²	1	2	yes	complemented
41	#557	C₂²	1	2	yes	complemented
42	#556	C₂²	1	1	yes	characteristic, complemented
43	#556	C₂²	1	2	yes	complemented
44	#556	C₂²	1	4	yes	complemented
45	#555	C₂²	1	1	yes	characteristic, complemented
46	#555	C₂²	1	4	yes	complemented
47	#554	C₂²	1	1	yes	characteristic, complemented
48	#554	C₂²	1	2	yes	complemented
49	#554	C₂²	1	4	yes	complemented
50	#553	C₂²	1	2	yes	complemented
51	#553	C₂²	1	4	yes	complemented
52	#553	C₂²	1	4	yes	complemented
53	#553	C₂²	1	8	yes	complemented
54	#553	C₂²	1	4	yes	complemented
55	#553	C₂²	1	8	yes	complemented
56	#553	C₂²	1	8	yes	complemented
57	#552	C₂²	1	2	yes	complemented
58	#552	C₂²	1	2	yes	complemented
59	#552	C₂²	1	4	yes	complemented
60	#551	C₂²	1	4	yes	complemented
61	#551	C₂²	1	8	yes	complemented
62	#551	C₂²	1	8	yes	complemented
63	#550	C₂²	1	2	yes	complemented
64	#550	C₂²	1	2	yes	complemented
65	#550	C₂²	1	4	yes	complemented
66	#550	C₂²	1	2	yes	complemented
67	#550	C₂²	1	2	yes	complemented
68	#550	C₂²	1	4	yes	complemented
69	#550	C₂²	1	1	yes	characteristic, complemented
70	#550	C₂²	1	4	yes	complemented
71	#550	C₂²	1	2	yes	complemented
72	#550	C₂²	1	2	yes	complemented
73	#550	C₂²	1	2	yes	complemented
74	#550	C₂²	1	4	yes	complemented
75	#550	C₂²	1	2	yes	complemented
76	#550	C₂²	1	4	yes	complemented
77	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
78	#548	C₂²	1	2	yes	complemented
79	#548	C₂²	1	4	yes	complemented
80	#547	C₂²	1	2	yes	complemented
81	#547	C₂²	1	1	yes	characteristic, complemented
82	#547	C₂²	1	1	yes	characteristic, complemented
83	#547	C₂²	1	4	yes	complemented
84	#547	C₂²	1	4	yes	complemented
85	#547	C₂²	1	4	yes	complemented
86	#547	C₂²	1	4	yes	complemented
87	#547	C₂²	1	4	yes	complemented
88	#546	C₂²	1	4	yes	complemented
89	#546	C₂²	1	2	yes	complemented
90	#546	C₂²	1	2	yes	complemented
91	#546	C₂²	1	4	yes	complemented
92	#546	C₂²	1	4	yes	complemented
93	#546	C₂²	1	4	yes	complemented
94	#546	C₂²	1	4	yes	complemented
95	#546	C₂²	1	4	yes	complemented
96	#546	C₂²	1	8	yes	complemented
97	#546	C₂²	1	8	yes	complemented
98	#546	C₂²	1	4	yes	complemented
99	#546	C₂²	1	4	yes	complemented
100	#546	C₂²	1	8	yes	complemented
101	#546	C₂²	1	4	yes	complemented
102	#546	C₂²	1	8	yes	complemented
103	D₄²	C₂²	1	1	yes	characteristic, complemented
104	D₄²	C₂²	1	2	yes	complemented
105	D₄²	C₂²	1	8	yes	complemented
106	D₄²	C₂²	1	4	yes	complemented
107	D₄²	C₂²	1	4	yes	complemented
108	D₄²	C₂²	1	2	yes	complemented
109	D₄²	C₂²	1	4	yes	complemented
110	D₄²	C₂²	1	2	yes	complemented
111	D₄²	C₂²	1	4	yes	complemented
112	#544	C₂²	1	1	yes	characteristic, complemented
113	#542	C₂²	1	2	yes	complemented
114	#542	C₂²	1	2	yes	complemented
115	#542	C₂²	1	4	yes	complemented
116	#542	C₂²	1	4	yes	complemented
117	#541	C₂²	1	2	yes	complemented
118	#541	C₂²	1	2	yes	complemented
119	#540	C₂²	1	4	yes	complemented
120	#540	C₂²	1	8	yes	complemented
121	#540	C₂²	1	4	yes	complemented
122	#540	C₂²	1	4	yes	complemented
123	#540	C₂²	1	8	yes	complemented
124	#540	C₂²	1	4	yes	complemented
125	#540	C₂²	1	4	yes	complemented
126	#540	C₂²	1	8	yes	complemented
127	#539	C₂²	1	4	yes	complemented
128	#539	C₂²	1	4	yes	complemented
129	#539	C₂²	1	8	yes	complemented
130	#539	C₂²	1	8	yes	complemented
131	#538	C₂²	1	8	yes	complemented
132	#538	C₂²	1	8	yes	complemented
133	#538	C₂²	1	8	yes	complemented
134	#538	C₂²	1	8	yes	complemented
135	#537	C₂²	1	1	yes	characteristic
136	#537	C₂²	1	4	yes	complemented
137	#537	C₂²	1	4	yes	complemented
138	#537	C₂²	1	4	yes	complemented
139	#537	C₂²	1	8	yes	complemented
140	#536	C₂²	1	1	yes	characteristic, complemented
141	#536	C₂²	1	2	yes	complemented
142	#536	C₂²	1	4	yes	complemented
143	#536	C₂²	1	1	yes	characteristic, complemented
144	#535	C₂²	1	2	yes	complemented
145	#535	C₂²	1	2	yes	complemented
146	#535	C₂²	1	4	yes	complemented
147	#535	C₂²	1	4	yes	complemented
148	#535	C₂²	1	4	yes	complemented
149	#535	C₂²	1	4	yes	complemented
150	#535	C₂²	1	4	yes	complemented
151	#535	C₂²	1	8	yes	complemented
152	#534	C₂²	1	8	yes	complemented
153	#534	C₂²	1	8	yes	complemented
154	#534	C₂²	1	8	yes	complemented
155	#533	C₂²	1	2	yes	complemented
156	#533	C₂²	1	2	yes	complemented
157	#533	C₂²	1	1	yes	characteristic, complemented
158	#532	C₂²	1	1	yes	characteristic
159	#532	C₂²	1	4	yes	complemented
160	#532	C₂²	1	4	yes	complemented
161	#532	C₂²	1	2	yes	complemented
162	#532	C₂²	1	4	yes	complemented
163	#532	C₂²	1	2	yes	complemented
164	#532	C₂²	1	2	yes	complemented
165	#532	C₂²	1	2	yes	complemented
166	C₂×#127	C₂²	1	1	yes	characteristic, complemented
167	C₂×#127	C₂²	1	2	yes	complemented
168	C₂×#127	C₂²	1	2	yes	complemented
169	#529	C₂²	1	4	yes	complemented
170	#529	C₂²	1	2	yes	complemented
171	#529	C₂²	1	2	yes	complemented
172	#529	C₂²	1	2	yes	complemented
173	#529	C₂²	1	4	yes	complemented
174	#529	C₂²	1	4	yes	complemented
175	#529	C₂²	1	4	yes	complemented
176	#525	C₂²	1	4	yes	complemented
177	#525	C₂²	1	8	yes	complemented
178	#525	C₂²	1	4	yes	complemented
179	#525	C₂²	1	2	yes	complemented
180	#525	C₂²	1	4	yes	complemented
181	#525	C₂²	1	2	yes	complemented
182	#525	C₂²	1	4	yes	complemented
183	C₂×#123	C₂²	1	8	yes	complemented
184	C₂×#121	C₂²	1	2	yes	complemented
185	C₂×#121	C₂²	1	4	yes	complemented
186	C₂×#121	C₂²	1	4	yes	complemented
187	#520	C₂²	1	2	yes	complemented
188	#520	C₂²	1	4	yes	complemented
189	#518	C₂²	1	2	yes	complemented
190	#518	C₂²	1	4	yes	complemented
191	C₄×#41	C₂²	1	1	yes	characteristic, complemented
192	C₄×#41	C₂²	1	1	yes	characteristic, complemented
193	C₄×#41	C₂²	1	2	yes	complemented
194	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
195	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄×D₄	C₂²	1	2	yes	complemented
197	C₂×C₄×D₄	C₂²	1	2	yes	complemented
198	C₂×#117	C₂²	1	2	yes	complemented
199	H(5,𝔽₂)	—	4	8	no	—
200	C₂×#41	—	4	8	no	—
201	C₂×#41	—	4	8	no	—
202	C₂×#41	C₂³	1	1	yes	characteristic
203	C₂×#41	C₂³	1	1	yes	characteristic
204	C₂×#41	C₂³	1	2	yes	—
205	C₂×#41	C₂³	1	2	yes	—
206	C₂×#41	C₂³	1	4	yes	—
207	C₂×#41	C₂³	1	4	yes	—
208	C₂×#41	C₂³	1	4	yes	—
209	C₂×#41	C₂³	1	4	yes	—
210	C₂×#41	C₂³	1	4	yes	—
211	C₂×#41	C₂³	1	2	yes	—
212	C₂×#41	C₂³	1	4	yes	—
213	C₂×#41	C₂³	1	2	yes	—
214	C₂×#41	C₂³	1	4	yes	—
215	C₂×#41	C₂³	1	4	yes	—
216	C₂×#41	C₂³	1	4	yes	—
217	C₂×#41	C₂³	1	8	yes	—
218	C₂×#41	C₂³	1	4	yes	—
219	C₂²×Q₈	C₂³	1	1	yes	characteristic
220	C₂²×Q₈	C₂³	1	2	yes	—
221	C₂²×D₄	C₂³	1	2	yes	—
222	C₂²×D₄	C₂³	1	1	yes	characteristic
223	C₂²×D₄	C₂³	1	2	yes	—
224	C₂²×D₄	C₂³	1	2	yes	—
225	C₂²×D₄	C₂³	1	4	yes	—
226	C₂²×D₄	C₂³	1	4	yes	—
227	C₂²×D₄	C₂³	1	4	yes	—
228	C₂²×D₄	C₂³	1	8	yes	—
229	C₂²×D₄	C₂³	1	4	yes	—
230	C₂²×D₄	C₂³	1	4	yes	—
231	C₂²×D₄	C₂³	1	2	yes	—
232	C₂²×D₄	C₂³	1	2	yes	—
233	C₂²×D₄	C₂³	1	4	yes	—
234	C₂²×D₄	C₂³	1	8	yes	—
235	C₂²×D₄	C₂³	1	4	yes	—
236	C₂³×C₄	C₂³	1	2	yes	—
237	C₂³×C₄	C₂³	1	4	yes	—
238	C₂³×C₄	C₂³	1	4	yes	—
239	C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈	C₂³	1	2	yes	—
241	C₄⋊Q₈	C₂³	1	2	yes	—
242	C₄⋊Q₈	C₂³	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³	1	4	yes	—
245	C₄⋊Q₈	C₂³	1	2	yes	—
246	C₄⋊Q₈	C₂³	1	2	yes	—
247	C₄⋊Q₈	C₂³	1	2	yes	—
248	#127	C₂³	1	1	yes	characteristic
249	#127	C₂³	1	2	yes	—
250	#127	C₂³	1	4	yes	—
251	#127	C₂³	1	2	yes	—
252	#127	C₂³	1	2	yes	—
253	#127	C₂³	1	4	yes	—
254	#127	C₂³	1	4	yes	—
255	#127	C₂³	1	4	yes	—
256	#127	C₂³	1	8	yes	—
257	#127	C₂³	1	2	yes	—
258	#127	C₂³	1	4	yes	—
259	#127	C₂³	1	2	yes	—
260	#127	C₂³	1	4	yes	—
261	#127	C₂³	1	8	yes	—
262	#126	C₂³	1	4	yes	—
263	#126	C₂³	1	4	yes	—
264	#126	C₂³	1	4	yes	—
265	#126	C₂³	1	8	yes	—
266	#126	C₂³	1	8	yes	—
267	#126	C₂³	1	4	yes	—
268	#126	C₂³	1	4	yes	—
269	#126	C₂³	1	4	yes	—
270	#126	C₂³	1	4	yes	—
271	#126	C₂³	1	8	yes	—
272	#126	C₂³	1	8	yes	—
273	#125	C₂³	1	2	yes	—
274	#125	C₂³	1	4	yes	—
275	#125	C₂³	1	4	yes	—
276	#125	C₂³	1	2	yes	—
277	#125	C₂³	1	4	yes	—
278	#125	C₂³	1	2	yes	—
279	#125	C₂³	1	4	yes	—
280	#125	C₂³	1	4	yes	—
281	#125	C₂³	1	2	yes	—
282	#125	C₂³	1	8	yes	—
283	#124	C₂³	1	2	yes	—
284	#124	C₂³	1	4	yes	—
285	#124	C₂³	1	4	yes	—
286	#124	C₂³	1	2	yes	—
287	#124	C₂³	1	4	yes	—
288	#124	C₂³	1	2	yes	—
289	#124	C₂³	1	4	yes	—
290	#124	C₂³	1	2	yes	—
291	#124	C₂³	1	4	yes	—
292	#124	C₂³	1	4	yes	—
293	#124	C₂³	1	4	yes	—
294	#124	C₂³	1	4	yes	—
295	#124	C₂³	1	8	yes	—
296	#124	C₂³	1	4	yes	—
297	#124	C₂³	1	8	yes	—
298	#124	C₂³	1	8	yes	—
299	#123	C₂³	1	4	yes	—
300	#123	C₂³	1	4	yes	—
301	#123	C₂³	1	4	yes	—
302	#123	C₂³	1	8	yes	—
303	#123	C₂³	1	8	yes	—
304	#123	C₂³	1	8	yes	—
305	#123	C₂³	1	8	yes	—
306	#123	C₂³	1	8	yes	—
307	#123	C₂³	1	4	yes	—
308	#123	C₂³	1	8	yes	—
309	#123	C₂³	1	8	yes	—
310	#123	C₂³	1	4	yes	—
311	#123	C₂³	1	8	yes	—
312	#123	C₂³	1	4	yes	—
313	#123	C₂³	1	4	yes	—
314	#123	C₂³	1	4	yes	—
315	#123	C₂³	1	4	yes	—
316	#123	C₂³	1	4	yes	—
317	#123	C₂³	1	8	yes	—
318	#123	C₂³	1	4	yes	—
319	#123	C₂³	1	8	yes	—
320	#123	C₂³	1	8	yes	—
321	#123	C₂³	1	8	yes	—
322	#123	C₂³	1	8	yes	—
323	#123	C₂³	1	8	yes	—
324	#123	C₂³	1	8	yes	—
325	#123	C₂³	1	8	yes	—
326	#123	C₂³	1	8	yes	—
327	C₂²⋊Q₈	C₂³	1	2	yes	—
328	C₂²⋊Q₈	C₂³	1	2	yes	—
329	C₂²⋊Q₈	C₂³	1	2	yes	—
330	C₂²⋊Q₈	C₂³	1	2	yes	—
331	C₂²⋊Q₈	C₂³	1	2	yes	—
332	C₂²⋊Q₈	C₂³	1	8	yes	—
333	C₂²⋊Q₈	C₂³	1	4	yes	—
334	C₂²⋊Q₈	C₂³	1	4	yes	—
335	C₂²⋊Q₈	C₂³	1	8	yes	—
336	C₂²⋊Q₈	C₂³	1	2	yes	—
337	C₂²⋊Q₈	C₂³	1	4	yes	—
338	C₂²⋊Q₈	C₂³	1	4	yes	—
339	C₂²⋊Q₈	C₂³	1	2	yes	—
340	C₂²⋊Q₈	C₂³	1	2	yes	—
341	C₂²⋊Q₈	C₂³	1	2	yes	—
342	C₂²⋊Q₈	C₂³	1	4	yes	—
343	C₂²⋊Q₈	C₂³	1	4	yes	—
344	C₂²⋊Q₈	C₂³	1	2	yes	—
345	C₂²⋊Q₈	C₂³	1	2	yes	—
346	C₂²⋊Q₈	C₂³	1	2	yes	—
347	C₂²⋊Q₈	C₂³	1	4	yes	—
348	C₂²⋊Q₈	C₂³	1	2	yes	—
349	C₂²⋊Q₈	C₂³	1	4	yes	—
350	C₂²⋊Q₈	C₂³	1	8	yes	—
351	C₂²⋊Q₈	C₂³	1	8	yes	—
352	C₂²⋊Q₈	C₂³	1	8	yes	—
353	#121	C₂³	1	2	yes	—
354	#121	C₂³	1	4	yes	—
355	#121	C₂³	1	2	yes	—
356	#121	C₂³	1	4	yes	—
357	#121	C₂³	1	4	yes	—
358	#121	C₂³	1	8	yes	—
359	#121	C₂³	1	4	yes	—
360	#121	C₂³	1	8	yes	—
361	#121	C₂³	1	8	yes	—
362	#121	C₂³	1	8	yes	—
363	#121	C₂³	1	8	yes	—
364	#121	C₂³	1	8	yes	—
365	#121	C₂³	1	4	yes	—
366	#121	C₂³	1	4	yes	—
367	#121	C₂³	1	2	yes	—
368	#121	C₂³	1	8	yes	—
369	#121	C₂³	1	2	yes	—
370	#121	C₂³	1	4	yes	—
371	#121	C₂³	1	4	yes	—
372	#121	C₂³	1	8	yes	—
373	#121	C₂³	1	2	yes	—
374	#121	C₂³	1	4	yes	—
375	#121	C₂³	1	4	yes	—
376	#121	C₂³	1	2	yes	—
377	#121	C₂³	1	4	yes	—
378	#121	C₂³	1	4	yes	—
379	#121	C₂³	1	2	yes	—
380	#121	C₂³	1	2	yes	—
381	#121	C₂³	1	2	yes	—
382	#121	C₂³	1	8	yes	—
383	#121	C₂³	1	8	yes	—
384	#121	C₂³	1	8	yes	—
385	#121	C₂³	1	8	yes	—
386	#121	C₂³	1	8	yes	—
387	#121	C₂³	1	4	yes	—
388	#121	C₂³	1	4	yes	—
389	#121	C₂³	1	4	yes	—
390	#121	C₂³	1	2	yes	—
391	#121	C₂³	1	4	yes	—
392	#121	C₂³	1	2	yes	—
393	#121	C₂³	1	4	yes	—
394	#121	C₂³	1	8	yes	—
395	#121	C₂³	1	8	yes	—
396	#121	C₂³	1	8	yes	—
397	#121	C₂³	1	8	yes	—
398	#121	C₂³	1	8	yes	—
399	#121	C₂³	1	8	yes	—
400	#121	C₂³	1	8	yes	—
401	#121	C₂³	1	8	yes	—
402	#121	C₂³	1	8	yes	—
403	#121	C₂³	1	8	yes	—
404	#121	C₂³	1	8	yes	—
405	#121	C₂³	1	8	yes	—
406	#121	C₂³	1	8	yes	—
407	#120	C₂³	1	8	yes	—
408	#120	C₂³	1	4	yes	—
409	#120	C₂³	1	4	yes	—
410	#120	C₂³	1	4	yes	—
411	#120	C₂³	1	8	yes	—
412	#120	C₂³	1	8	yes	—
413	#120	C₂³	1	8	yes	—
414	#120	C₂³	1	4	yes	—
415	#120	C₂³	1	8	yes	—
416	#120	C₂³	1	8	yes	—
417	#120	C₂³	1	8	yes	—
418	#120	C₂³	1	8	yes	—
419	#120	C₂³	1	8	yes	—
420	#120	C₂³	1	8	yes	—
421	#120	C₂³	1	8	yes	—
422	C₄×Q₈	C₂³	1	2	yes	—
423	C₄×Q₈	C₂³	1	2	yes	—
424	C₄×Q₈	C₂³	1	2	yes	—
425	C₄×Q₈	C₂³	1	2	yes	—
426	C₄×Q₈	C₂³	1	2	yes	—
427	C₄×Q₈	C₂³	1	2	yes	—
428	C₄×Q₈	C₂³	1	1	yes	characteristic
429	C₄×Q₈	C₂³	1	1	yes	characteristic
430	C₄×Q₈	C₂³	1	1	yes	characteristic
431	C₄×Q₈	C₂³	1	1	yes	characteristic
432	C₄×Q₈	C₂³	1	4	yes	—
433	C₄×Q₈	C₂³	1	4	yes	—
434	C₄×Q₈	C₂³	1	2	yes	—
435	C₄×Q₈	C₂³	1	4	yes	—
436	C₄×D₄	C₂³	1	1	yes	characteristic
437	C₄×D₄	C₂³	1	1	yes	characteristic
438	C₄×D₄	C₂³	1	2	yes	—
439	C₄×D₄	C₂³	1	4	yes	—
440	C₄×D₄	C₂³	1	4	yes	—
441	C₄×D₄	C₂³	1	2	yes	—
442	C₄×D₄	C₂³	1	1	yes	characteristic
443	C₄×D₄	C₂³	1	2	yes	—
444	C₄×D₄	C₂³	1	2	yes	—
445	C₄×D₄	C₂³	1	1	yes	characteristic
446	C₄×D₄	C₂³	1	4	yes	—
447	C₄×D₄	C₂³	1	8	yes	—
448	C₄×D₄	C₂³	1	2	yes	—
449	C₄×D₄	C₂³	1	4	yes	—
450	C₄×D₄	C₂³	1	4	yes	—
451	C₄×D₄	C₂³	1	2	yes	—
452	C₄×D₄	C₂³	1	1	yes	characteristic
453	C₄×D₄	C₂³	1	2	yes	—
454	C₄×D₄	C₂³	1	1	yes	characteristic
455	C₄×D₄	C₂³	1	2	yes	—
456	C₄×D₄	C₂³	1	2	yes	—
457	C₄×D₄	C₂³	1	4	yes	—
458	C₄×D₄	C₂³	1	2	yes	—
459	C₄×D₄	C₂³	1	1	yes	characteristic
460	C₄×D₄	C₂³	1	1	yes	characteristic
461	C₄×D₄	C₂³	1	8	yes	—
462	C₄×D₄	C₂³	1	4	yes	—
463	C₄×D₄	C₂³	1	4	yes	—
464	C₄×D₄	C₂³	1	4	yes	—
465	C₄×D₄	C₂³	1	4	yes	—
466	C₄×D₄	C₂³	1	4	yes	—
467	C₄×D₄	C₂³	1	8	yes	—
468	C₄×D₄	C₂³	1	4	yes	—
469	C₄×D₄	C₂³	1	8	yes	—
470	C₄×D₄	C₂³	1	8	yes	—
471	C₄×D₄	C₂³	1	8	yes	—
472	C₄×D₄	C₂³	1	4	yes	—
473	C₄×D₄	C₂³	1	4	yes	—
474	C₄×D₄	C₂³	1	2	yes	—
475	C₄×D₄	C₂³	1	4	yes	—
476	C₄×D₄	C₂³	1	8	yes	—
477	C₄×D₄	C₂³	1	8	yes	—
478	C₄×D₄	C₂³	1	4	yes	—
479	C₄×D₄	C₂³	1	8	yes	—
480	C₄×D₄	C₂³	1	4	yes	—
481	C₄×D₄	C₂³	1	8	yes	—
482	C₄×D₄	C₂³	1	4	yes	—
483	C₄×D₄	C₂³	1	4	yes	—
484	#117	C₂³	1	1	yes	characteristic
485	#117	C₂³	1	2	yes	—
486	#117	C₂³	1	4	yes	—
487	#117	C₂³	1	2	yes	—
488	#117	C₂³	1	2	yes	—
489	#117	C₂³	1	4	yes	—
490	#117	C₂³	1	1	yes	characteristic
491	#117	C₂³	1	2	yes	—
492	#117	C₂³	1	2	yes	—
493	#117	C₂³	1	2	yes	—
494	#117	C₂³	1	4	yes	—
495	#117	C₂³	1	4	yes	—
496	#117	C₂³	1	4	yes	—
497	#117	C₂³	1	4	yes	—
498	#117	C₂³	1	8	yes	—
499	#117	C₂³	1	8	yes	—
500	C₂×C₄⋊C₄	C₂³	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³	1	8	yes	—
508	C₂×C₄⋊C₄	C₂³	1	8	yes	—
509	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
514	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
515	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
516	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
517	C₂×C₄²	C₂³	1	4	yes	—
518	C₂×C₄²	C₂³	1	1	yes	characteristic
519	C₂×C₄²	C₂³	1	2	yes	—
520	C₂×C₄²	C₂³	1	2	yes	—
521	C₂×C₄²	C₂³	1	2	yes	—
522	C₂⁴	C₂⁴	1	2	yes	—
523	C₂⁴	C₂⁴	1	4	yes	—
524	C₂⁴	C₂⁴	1	8	yes	—
525	C₂⁴	C₂⁴	1	4	yes	—
526	#41	—	2	4	no	—
527	#41	—	2	8	no	—
528	#41	—	2	4	no	—
529	#41	—	4	8	no	—
530	#41	—	4	8	no	—
531	#41	—	4	8	no	—
532	#41	—	4	8	no	—
533	#41	—	4	8	no	—
534	#41	—	4	8	no	—
535	#41	—	4	4	no	—
536	#41	—	4	4	no	—
537	#41	—	4	4	no	—
538	#41	—	4	8	no	—
539	#41	—	4	8	no	—
540	#41	—	4	8	no	—
541	#41	—	8	8	no	—
542	#41	—	8	4	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	4	4	no	—
545	C₂×Q₈	C₂⁴	1	2	yes	—
546	C₂×Q₈	C₂⁴	1	2	yes	—
547	C₂×Q₈	C₂⁴	1	1	yes	characteristic
548	C₂×Q₈	C₂⁴	1	1	yes	characteristic
549	C₂×Q₈	C₂⁴	1	2	yes	—
550	C₂×Q₈	C₂⁴	1	2	yes	—
551	C₂×Q₈	C₂⁴	1	2	yes	—
552	C₂×Q₈	C₂⁴	1	4	yes	—
553	C₂×Q₈	C₂⁴	1	4	yes	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	8	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	8	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	8	no	—
563	C₂×D₄	—	4	8	no	—
564	C₂×D₄	—	4	16	no	—
565	C₂×D₄	—	8	2	no	—
566	C₂×D₄	—	8	4	no	—
567	C₂×D₄	—	8	4	no	—
568	C₂×D₄	—	8	8	no	—
569	C₂×D₄	C₂⁴	1	1	yes	characteristic
570	C₂×D₄	C₂⁴	1	2	yes	—
571	C₂×D₄	C₂⁴	1	4	yes	—
572	C₂×D₄	C₂⁴	1	1	yes	characteristic
573	C₂×D₄	C₂⁴	1	2	yes	—
574	C₂×D₄	C₂⁴	1	4	yes	—
575	C₂×D₄	C₂⁴	1	2	yes	—
576	C₂×D₄	C₂⁴	1	1	yes	characteristic
577	C₂×D₄	C₂⁴	1	4	yes	—
578	C₂×D₄	C₂⁴	1	2	yes	—
579	C₂×D₄	C₂⁴	1	4	yes	—
580	C₂×D₄	C₂⁴	1	1	yes	characteristic
581	C₂×D₄	C₂⁴	1	4	yes	—
582	C₂×D₄	C₂⁴	1	4	yes	—
583	C₂×D₄	C₂⁴	1	8	yes	—
584	C₂×D₄	C₂⁴	1	8	yes	—
585	C₂×D₄	C₂⁴	1	2	yes	—
586	C₂×D₄	C₂⁴	1	4	yes	—
587	C₂×D₄	C₂⁴	1	4	yes	—
588	C₂×D₄	C₂⁴	1	4	yes	—
589	C₂×D₄	C₂⁴	1	8	yes	—
590	C₂×D₄	C₂⁴	1	8	yes	—
591	C₂×D₄	C₂⁴	1	4	yes	—
592	C₂×D₄	C₂⁴	1	4	yes	—
593	C₂×D₄	C₂⁴	1	2	yes	—
594	C₂×D₄	C₂⁴	1	8	yes	—
595	C₂×D₄	C₂⁴	1	8	yes	—
596	C₂×D₄	C₂⁴	1	4	yes	—
597	C₂×D₄	C₂⁴	1	4	yes	—
598	C₂×D₄	C₂⁴	1	8	yes	—
599	C₂×D₄	C₂⁴	1	4	yes	—
600	C₂×D₄	C₂⁴	1	8	yes	—
601	C₂×D₄	C₂⁴	1	4	yes	—
602	C₂×D₄	C₂⁴	1	8	yes	—
603	C₂×D₄	C₂⁴	1	8	yes	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	4	8	no	—
606	C₂²×C₄	—	4	8	no	—
607	C₂²×C₄	C₂⁴	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴	1	2	yes	—
609	C₂²×C₄	C₂⁴	1	2	yes	—
610	C₂²×C₄	C₂⁴	1	2	yes	—
611	C₂²×C₄	C₂⁴	1	2	yes	—
612	C₂²×C₄	C₂⁴	1	2	yes	—
613	C₂²×C₄	C₂⁴	1	2	yes	—
614	C₂²×C₄	C₂⁴	1	2	yes	—
615	C₂²×C₄	C₂⁴	1	2	yes	—
616	C₂²×C₄	C₂⁴	1	4	yes	—
617	C₂²×C₄	C₂⁴	1	2	yes	—
618	C₂²×C₄	C₂⁴	1	2	yes	—
619	C₂²×C₄	C₂⁴	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴	1	2	yes	—
621	C₂²×C₄	C₂⁴	1	2	yes	—
622	C₂²×C₄	C₂⁴	1	4	yes	—
623	C₂²×C₄	C₂⁴	1	4	yes	—
624	C₂²×C₄	C₂⁴	1	2	yes	—
625	C₂²×C₄	C₂⁴	1	8	yes	—
626	C₂²×C₄	C₂⁴	1	8	yes	—
627	C₂²×C₄	C₂⁴	1	4	yes	—
628	C₂²×C₄	C₂⁴	1	8	yes	—
629	C₂²×C₄	C₂⁴	1	4	yes	—
630	C₂²×C₄	C₂⁴	1	8	yes	—
631	C₂²×C₄	C₂⁴	1	8	yes	—
632	C₂²×C₄	C₂⁴	1	8	yes	—
633	C₂²×C₄	C₂⁴	1	4	yes	—
634	C₂²×C₄	C₂⁴	1	1	yes	characteristic
635	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
636	C₄⋊C₄	C₂⁴	1	2	yes	—
637	C₄⋊C₄	C₂⁴	1	4	yes	—
638	C₄⋊C₄	C₂⁴	1	2	yes	—
639	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴	1	4	yes	—
642	C₄⋊C₄	C₂⁴	1	4	yes	—
643	C₄⋊C₄	C₂⁴	1	4	yes	—
644	C₄⋊C₄	C₂⁴	1	4	yes	—
645	C₄⋊C₄	C₂⁴	1	4	yes	—
646	C₄⋊C₄	C₂⁴	1	2	yes	—
647	C₄⋊C₄	C₂⁴	1	4	yes	—
648	C₄⋊C₄	C₂⁴	1	4	yes	—
649	C₄⋊C₄	C₂⁴	1	8	yes	—
650	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₄⋊C₄	C₂⁴	1	2	yes	—
652	C₄⋊C₄	C₂⁴	1	2	yes	—
653	C₄⋊C₄	C₂⁴	1	2	yes	—
654	C₄⋊C₄	C₂⁴	1	8	yes	—
655	C₄⋊C₄	C₂⁴	1	8	yes	—
656	C₄⋊C₄	C₂⁴	1	4	yes	—
657	C₄⋊C₄	C₂⁴	1	4	yes	—
658	C₄⋊C₄	C₂⁴	1	4	yes	—
659	C₄⋊C₄	C₂⁴	1	4	yes	—
660	C₄⋊C₄	C₂⁴	1	2	yes	—
661	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
662	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
663	C₄⋊C₄	C₂⁴	1	4	yes	—
664	C₄⋊C₄	C₂⁴	1	4	yes	—
665	C₄⋊C₄	C₂⁴	1	2	yes	—
666	C₄⋊C₄	C₂⁴	1	2	yes	—
667	C₄⋊C₄	C₂⁴	1	2	yes	—
668	C₄⋊C₄	C₂⁴	1	2	yes	—
669	C₄⋊C₄	C₂⁴	1	4	yes	—
670	C₄⋊C₄	C₂⁴	1	2	yes	—
671	C₄⋊C₄	C₂⁴	1	4	yes	—
672	C₄⋊C₄	C₂⁴	1	4	yes	—
673	C₄⋊C₄	C₂⁴	1	4	yes	—
674	C₄⋊C₄	C₂⁴	1	2	yes	—
675	C₂²⋊C₄	C₂⁴	1	2	yes	—
676	C₂²⋊C₄	C₂⁴	1	4	yes	—
677	C₂²⋊C₄	C₂⁴	1	4	yes	—
678	C₂²⋊C₄	C₂⁴	1	2	yes	—
679	C₂²⋊C₄	C₂⁴	1	4	yes	—
680	C₂²⋊C₄	C₂⁴	1	2	yes	—
681	C₂²⋊C₄	C₂⁴	1	8	yes	—
682	C₂²⋊C₄	C₂⁴	1	4	yes	—
683	C₂²⋊C₄	C₂⁴	1	4	yes	—
684	C₂²⋊C₄	C₂⁴	1	4	yes	—
685	C₂²⋊C₄	C₂⁴	1	4	yes	—
686	C₂²⋊C₄	C₂⁴	1	4	yes	—
687	C₂²⋊C₄	C₂⁴	1	2	yes	—
688	C₂²⋊C₄	C₂⁴	1	4	yes	—
689	C₂²⋊C₄	C₂⁴	1	4	yes	—
690	C₂²⋊C₄	C₂⁴	1	8	yes	—
691	C₂²⋊C₄	C₂⁴	1	2	yes	—
692	C₂²⋊C₄	C₂⁴	1	4	yes	—
693	C₂²⋊C₄	C₂⁴	1	8	yes	—
694	C₂²⋊C₄	C₂⁴	1	4	yes	—
695	C₂²⋊C₄	C₂⁴	1	8	yes	—
696	C₂²⋊C₄	C₂⁴	1	8	yes	—
697	C₂²⋊C₄	C₂⁴	1	8	yes	—
698	C₂²⋊C₄	C₂⁴	1	8	yes	—
699	C₂²⋊C₄	C₂⁴	1	2	yes	—
700	C₂²⋊C₄	C₂⁴	1	4	yes	—
701	C₂²⋊C₄	C₂⁴	1	2	yes	—
702	C₂²⋊C₄	C₂⁴	1	2	yes	—
703	C₂²⋊C₄	C₂⁴	1	8	yes	—
704	C₂²⋊C₄	C₂⁴	1	4	yes	—
705	C₂²⋊C₄	C₂⁴	1	4	yes	—
706	C₂²⋊C₄	C₂⁴	1	8	yes	—
707	C₂²⋊C₄	C₂⁴	1	2	yes	—
708	C₂²⋊C₄	C₂⁴	1	2	yes	—
709	C₂²⋊C₄	C₂⁴	1	4	yes	—
710	C₂²⋊C₄	C₂⁴	1	4	yes	—
711	C₂²⋊C₄	C₂⁴	1	4	yes	—
712	C₂²⋊C₄	C₂⁴	1	8	yes	—
713	C₂²⋊C₄	C₂⁴	1	8	yes	—
714	C₂²⋊C₄	C₂⁴	1	4	yes	—
715	C₄²	C₂⁴	1	2	yes	—
716	C₄²	C₂⁴	1	1	yes	characteristic
717	C₄²	C₂⁴	1	1	yes	characteristic
718	C₄²	C₂⁴	1	4	yes	—
719	C₄²	C₂⁴	1	4	yes	—
720	C₄²	C₂⁴	1	2	yes	—
721	C₄²	C₂⁴	1	4	yes	—
722	C₄²	C₂⁴	1	2	yes	—
723	C₄²	C₂⁴	1	1	yes	characteristic
724	C₄²	C₂⁴	1	2	yes	—
725	C₄²	C₂⁴	1	4	yes	—
726	C₄²	C₂⁴	1	1	yes	characteristic
727	C₄²	C₂⁴	1	2	yes	—
728	C₄²	C₂⁴	1	4	yes	—
729	C₄²	C₂⁴	1	2	yes	—
730	C₄²	C₂⁴	1	8	yes	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	8	no	—
733	C₂³	—	4	4	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	8	no	—
743	C₂³	C₂⁵	1	2	yes	—
744	C₂³	C₂⁵	1	2	yes	—
745	C₂³	C₂⁵	1	4	yes	—
746	C₂³	C₂⁵	1	2	yes	—
747	C₂³	C₂⁵	1	8	yes	—
748	C₂³	C₂⁵	1	2	yes	—
749	C₂³	C₂⁵	1	1	yes	characteristic
750	Q₈	—	2	4	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	4	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	4	no	—
756	Q₈	—	4	4	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	D₄	—	2	4	no	—
760	D₄	—	2	8	no	—
761	D₄	—	2	4	no	—
762	D₄	—	2	8	no	—
763	D₄	—	2	8	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	4	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	8	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	2	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	8	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	8	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
822	C₂×C₄	C₂⁵	1	1	yes	characteristic
823	C₂×C₄	C₂⁵	1	4	yes	—
824	C₂×C₄	C₂⁵	1	2	yes	—
825	C₂×C₄	C₂⁵	1	2	yes	—
826	C₂×C₄	C₂⁵	1	1	yes	characteristic
827	C₂×C₄	C₂⁵	1	2	yes	—
828	C₂×C₄	C₂⁵	1	4	yes	—
829	C₂×C₄	C₂⁵	1	1	yes	characteristic
830	C₂×C₄	C₂⁵	1	2	yes	—
831	C₂×C₄	C₂⁵	1	2	yes	—
832	C₂×C₄	C₂⁵	1	4	yes	—
833	C₂×C₄	C₂⁵	1	2	yes	—
834	C₂×C₄	C₂⁵	1	4	yes	—
835	C₂×C₄	C₂⁵	1	4	yes	—
836	C₂×C₄	C₂⁵	1	2	yes	—
837	C₂×C₄	C₂⁵	1	2	yes	—
838	C₂×C₄	C₂⁵	1	1	yes	characteristic
839	C₂×C₄	C₂⁵	1	1	yes	characteristic
840	C₂×C₄	C₂⁵	1	1	yes	characteristic
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	8	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	8	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	8	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	8	4	no	—
862	C₂²	—	8	8	no	—
863	C₂²	—	8	8	no	—
864	C₂²	—	16	8	no	—
865	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
866	C₂²	C₂⁶	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	4	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	4	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	4	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	2	no	—
883	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
884	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
885	C₄	#585	1	2	yes	—
886	C₂	—	2	2	no	—
887	C₂	—	4	2	no	—
888	C₂	—	4	2	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	8	no	—
891	C₂	—	4	4	no	—
892	C₂	—	4	2	no	—
893	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
894	C₂	C₂×#585	1	1	yes	characteristic
895	C₂	H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #3562	C₂	semidirect
2. #3554	C₂	semidirect
3. #3548	C₂	semidirect
4. #3546	C₂	semidirect
5. #3546	C₂	semidirect
6. #3543	C₂	semidirect
7. #3543	C₂	semidirect
8. #3542	C₂	semidirect
9. #3539	C₂	semidirect
10. #3534	C₂	semidirect
11. #3519	C₂	semidirect
12. #3517	C₂	semidirect
13. #3513	C₂	semidirect
14. #3508	C₂	semidirect
15. #3508	C₂	semidirect
16. #3507	C₂	semidirect
17. #3506	C₂	semidirect
18. #3498	C₂	semidirect
19. #3494	C₂	semidirect
20. #3488	C₂	semidirect
21. #3485	C₂	semidirect
22. #3475	C₂	semidirect
23. D₄×#41	C₂	semidirect
24. C₂×#550	C₂	semidirect
25. #3461	C₂	semidirect
26. #3449	C₂	semidirect
27. C₂×H(5,𝔽₂)	C₂²	semidirect
28. C₂²×#41	C₂²	semidirect
29. C₂²×#41	C₂²	semidirect
30. #562	C₂²	semidirect
31. #562	C₂²	semidirect
32. #560	C₂²	semidirect
33. #560	C₂²	semidirect
34. #560	C₂²	semidirect
35. #560	C₂²	semidirect
36. #559	C₂²	semidirect
37. #559	C₂²	semidirect
38. #559	C₂²	semidirect
39. #559	C₂²	semidirect
40. #559	C₂²	semidirect
41. #557	C₂²	semidirect
42. #556	C₂²	semidirect
43. #556	C₂²	semidirect
44. #556	C₂²	semidirect
45. #555	C₂²	semidirect
46. #555	C₂²	semidirect
47. #554	C₂²	semidirect
48. #554	C₂²	semidirect
49. #554	C₂²	semidirect
50. #553	C₂²	semidirect
51. #553	C₂²	semidirect
52. #553	C₂²	semidirect
53. #553	C₂²	semidirect
54. #553	C₂²	semidirect
55. #553	C₂²	semidirect
56. #553	C₂²	semidirect
57. #552	C₂²	semidirect
58. #552	C₂²	semidirect
59. #552	C₂²	semidirect
60. #551	C₂²	semidirect
61. #551	C₂²	semidirect
62. #551	C₂²	semidirect
63. #550	C₂²	semidirect
64. #550	C₂²	semidirect
65. #550	C₂²	semidirect
66. #550	C₂²	semidirect
67. #550	C₂²	semidirect
68. #550	C₂²	semidirect
69. #550	C₂²	semidirect
70. #550	C₂²	semidirect
71. #550	C₂²	semidirect
72. #550	C₂²	semidirect
73. #550	C₂²	semidirect
74. #550	C₂²	semidirect
75. #550	C₂²	semidirect
76. #550	C₂²	semidirect
77. D₄×Q₈	C₂²	semidirect
78. #548	C₂²	semidirect
79. #548	C₂²	semidirect
80. #547	C₂²	semidirect
81. #547	C₂²	semidirect
82. #547	C₂²	semidirect
83. #547	C₂²	semidirect
84. #547	C₂²	semidirect
85. #547	C₂²	semidirect
86. #547	C₂²	semidirect
87. #547	C₂²	semidirect
88. #546	C₂²	semidirect
89. #546	C₂²	semidirect
90. #546	C₂²	semidirect
91. #546	C₂²	semidirect
92. #546	C₂²	semidirect
93. #546	C₂²	semidirect
94. #546	C₂²	semidirect
95. #546	C₂²	semidirect
96. #546	C₂²	semidirect
97. #546	C₂²	semidirect
98. #546	C₂²	semidirect
99. #546	C₂²	semidirect
100. #546	C₂²	semidirect
101. #546	C₂²	semidirect
102. #546	C₂²	semidirect
103. D₄²	C₂²	semidirect
104. D₄²	C₂²	semidirect
105. D₄²	C₂²	semidirect
106. D₄²	C₂²	semidirect
107. D₄²	C₂²	semidirect
108. D₄²	C₂²	semidirect
109. D₄²	C₂²	semidirect
110. D₄²	C₂²	semidirect
111. D₄²	C₂²	semidirect
112. #544	C₂²	semidirect
113. #542	C₂²	semidirect
114. #542	C₂²	semidirect
115. #542	C₂²	semidirect
116. #542	C₂²	semidirect
117. #541	C₂²	semidirect
118. #541	C₂²	semidirect
119. #540	C₂²	semidirect
120. #540	C₂²	semidirect
121. #540	C₂²	semidirect
122. #540	C₂²	semidirect
123. #540	C₂²	semidirect
124. #540	C₂²	semidirect
125. #540	C₂²	semidirect
126. #540	C₂²	semidirect
127. #539	C₂²	semidirect
128. #539	C₂²	semidirect
129. #539	C₂²	semidirect
130. #539	C₂²	semidirect
131. #538	C₂²	semidirect
132. #538	C₂²	semidirect
133. #538	C₂²	semidirect
134. #538	C₂²	semidirect
136. #537	C₂²	semidirect
137. #537	C₂²	semidirect
138. #537	C₂²	semidirect
139. #537	C₂²	semidirect
140. #536	C₂²	semidirect
141. #536	C₂²	semidirect
142. #536	C₂²	semidirect
143. #536	C₂²	semidirect
144. #535	C₂²	semidirect
145. #535	C₂²	semidirect
146. #535	C₂²	semidirect
147. #535	C₂²	semidirect
148. #535	C₂²	semidirect
149. #535	C₂²	semidirect
150. #535	C₂²	semidirect
151. #535	C₂²	semidirect
152. #534	C₂²	semidirect
153. #534	C₂²	semidirect
154. #534	C₂²	semidirect
155. #533	C₂²	semidirect
156. #533	C₂²	semidirect
157. #533	C₂²	semidirect
159. #532	C₂²	semidirect
160. #532	C₂²	semidirect
161. #532	C₂²	semidirect
162. #532	C₂²	semidirect
163. #532	C₂²	semidirect
164. #532	C₂²	semidirect
165. #532	C₂²	semidirect
166. C₂×#127	C₂²	semidirect
167. C₂×#127	C₂²	semidirect
168. C₂×#127	C₂²	semidirect
169. #529	C₂²	semidirect
170. #529	C₂²	semidirect
171. #529	C₂²	semidirect
172. #529	C₂²	semidirect
173. #529	C₂²	semidirect
174. #529	C₂²	semidirect
175. #529	C₂²	semidirect
176. #525	C₂²	semidirect
177. #525	C₂²	semidirect
178. #525	C₂²	semidirect
179. #525	C₂²	semidirect
180. #525	C₂²	semidirect
181. #525	C₂²	semidirect
182. #525	C₂²	semidirect
183. C₂×#123	C₂²	semidirect
184. C₂×#121	C₂²	semidirect
185. C₂×#121	C₂²	semidirect
186. C₂×#121	C₂²	semidirect
187. #520	C₂²	semidirect
188. #520	C₂²	semidirect
189. #518	C₂²	semidirect
190. #518	C₂²	semidirect
191. C₄×#41	C₂²	semidirect
192. C₄×#41	C₂²	semidirect
193. C₄×#41	C₂²	semidirect
194. C₂×C₄×Q₈	C₂²	semidirect
195. C₂×C₄×D₄	C₂²	semidirect
196. C₂×C₄×D₄	C₂²	semidirect
197. C₂×C₄×D₄	C₂²	semidirect
198. C₂×#117	C₂²	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3562	2
#3554	2
#3548	2
#3546	2
#3543	2
#3542	2
#3539	2
#3534	2
#3519	2
#3517	2
#3513	2
#3508	2
#3507	2
#3506	2
#3498	2
#3494	2
#3488	2
#3485	2
#3475	2
D₄×#41	2
C₂×#550	2
#3461	2
#3449	2